Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
import math
n=input()
for i in range(1,int(n**0.5)+1):
	a=((i*(i+1))/2.0)
	b=n-a
	c1=(-1+(1+8*b)**0.5)/2.0
	c2=(-1-(1+8*b)**0.5)/2.0
	if c1>0 and math.ceil(c1)==math.floor(c1):
		print 'YES'
		exit()
print 'NO'